Degree 1 Taylor on a interval

• \(R\) is the reference interval. The following numbering of the subentities of the reference is used:

• \(\mathcal{V}\) is spanned by: \(1\), \(x\)
• \(\mathcal{L}=\{l_0,...,l_{1}\}\)
• Functionals and basis functions:

\(\displaystyle l_{0}:v\mapsto\displaystyle\int_{R}v\)
where \(R\) is the reference element.

\(\displaystyle \phi_{0} = 1\)

This DOF is associated with edge 0 of the reference element.

\(\displaystyle l_{1}:v\mapsto v'(\tfrac{1}{2})\)

\(\displaystyle \phi_{1} = x - \frac{1}{2}\)

This DOF is associated with edge 0 of the reference element.